Hydrogen Spectrum Questions

The hydrogen spectrum is the spectrum of frequencies of electromagnetic radiation emitted due to an electron transition from a high energy state to a lower energy state. It depicts the quantized electronic structure of the hydrogen atom. Hydrogen atom depicts multiple lines in their line spectrum as they absorb diverse amounts of energy and goes to distinct excited states.

Hydrogen Spectrum Chemistry Questions with Solutions

Q1. The transition from the third shell to any other shell is known as

(a) Balmer series

(b) Paschen series

(c ) Pfund series

(d) None of the above

Answer: (b) The transition from the third shell to any other shell is known as Paschen series.

Q2. What is the term for band of colours?

(a) Dispersion

(b) Spectrum

(c ) Spectral lines

(d) None of the above

Answer: (b) Spectrum is the term for a band of colours.

Q3. The hydrogen emission spectrum comprises radiation of discrete

(a) Frequency

(b) Wavelength

(c ) Energy

(d) None of the above

Answer: (a) The hydrogen emission spectrum comprises radiation of discrete frequencies.

Q4. Atomic hydrogen displays

(a) Emission spectrum

(b) Absorption spectrum

(c ) Dispersion spectrum

(d) None of the above

Answer: (a) Atomic hydrogen displays emission spectrum.

Q5. Which spectral series of the hydrogen spectrum lies in the ultraviolet region?

(a) Lyman series

(b) Paschen series

(c ) Pfund series

(d) None of the above

Answer: (a) Lyman series of the hydrogen spectrum lies in the ultraviolet region.

Q6. What is the ratio of the energies of the hydrogen atom in its first to a second excited state?

Answer: 1st excited state corresponds to n = 2

2nd excited state corresponds to n = 3

Hence,

Hence, the ratio of the energies of the hydrogen atom in its first to a second excited state is equivalent to 9 / 4.

Q7. The ground state energy of the hydrogen atom is −13.6eV. What will be its potential energy?

Answer: The ground state energy of the hydrogen atom = − 13.6 eV

The kinetic energy of the hydrogen atom = – The ground state energy of the hydrogen atom

The kinetic energy of the hydrogen atom = 13.6 eV

The potential energy of the hydrogen atom = – 2 X (The kinetic energy of the hydrogen atom)

The potential energy of the hydrogen atom = – 2 X (13.6 eV)

The potential energy of the hydrogen atom = – 27.2 eV

Q8. What are the different series of hydrogen spectra?

Answer: The primary spectral series of hydrogen spectra are mentioned below.

1. Lyman series

2. Balmer series

3. Paschen series

4. Brackett series

5. Pfund series

6. Humphreys series

Q9. What will happen to Bohr’s formula of a Hydrogen atom if the proton acquires a charge of (+ 4 / 3 e) and the electron acquires a charge of (- 3 / 4) e where e = 1.6 X 10⁻¹⁹ C?

Answer: In accordance with Bohr’s model of an atom the electrostatic force supplies the required centripetal force fo the electron revolving around the stationary nucleus.

q₁q₂ / 4 πƐr² = mv² / r

Therefore, the electrostatic force is directly proportional to the q₁q_2.

If the proton acquires a charge of (+ 4 / 3 e) and the electron acquires a charge of (- 3 / 4) e, then Bohr’s formula of a Hydrogen atom will remain the same.

As the product of 3 / 4 and 4 / 3 is equivalent to unity.

Q10. State any two limitations of Bohr’s model of an atom.

Answer: Bohr’s model of an atom states that an atom has a tiny positively charged particle known as a nucleus surrounded by the negatively charged particle known as electrons. Electrons revolve around the nucleus in a fixed orbit.

The limitations of Bohr’s model of an atom are mentioned below.

1. He could not explain the structure of a large atom.

2. He could not explain the Zeeman effect.

Q11. Fetch an expression for the frequency of radiation emitted when a hydrogen atom deexcites from level n to level (n₁). For large n, show that this frequency equals the classical frequency of the revolution of the electron in orbit.

Answer:

For large n,

Orbital frequency v_e = (v / 2πr).

In the Bohr model,

This gives,

Which is the same for large n.

Q12. What is the wavelength of light emitted when the electron in a hydrogen atom transitions from an energy level with n = 4 to an energy level with n = 2?

Answer:

The expression for the wavelength of radiation is,

Substitute values in the above expression,

𝝀 = 4.86 X 10⁻⁵ cm

𝝀 = 486 X 10⁻⁹ m

𝝀 = 486 nm.

The line belongs to a bluish-green colour.

Q13. A hydrogen atom initially at the ground level absorbs a photon, which excites it to the n = 4 th level. Calculate the frequency and wavelength of the photon.

Answer:

For the ground level,

n₁ = 1

E₁ = – 13.67 / n₁²

E₁ = 13.67 eV

The atom is excited to a higher level, n₂ = 4

E₂ = – 13.67 / n₂²

E₂ = – 13.67 / 16 eV

E = E₁ – E₂

E = hc / 𝝀

𝝀 = hc / E₁ – E₂

𝝀 = 97 nm

c = 𝝀v

V = 3.1 X 10¹⁵ Hz.

Q14. Calculate the shortest and longest wavelengths in the hydrogen spectrum of the Lyman series.

Answer:

For the Lyman series, n₁ = 1.

For the shortest wavelength in the Lyman series (i.e., series limit), the energy difference in two states showing transition should be maximum, i.e., n₁ = infinity.

So,

𝝀 = 9.117 X 10^-6 cm

𝝀 = 911.7 A

For the longest wavelength in the Lyman series (i.e., first-line), the energy difference in two states showing transition should be minimum, i.e., n₂ = 2.

So,

Or

𝝀 = 1215.7 X 10^-8 cm

𝝀 = 1215.7 A

Q15. Match the following.

Answer:

Practise Questions on Hydrogen Spectrum

Q1. Describe Bohr’s model of an atom.

Q2. Explain Bohr’s postulates for the hydrogen atom model.

Q3. What is the quantisation of charge?

Q4. Explain the line spectrum of hydrogen.

Q5. Why are there multiple lines in the hydrogen line spectrum?

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